I'd recommend trying SQLite for logging. We've been doing this for a half decade and it's fantastic.

There's an index on our trace/correlation column, so we can instantly pull all log entries for a specific user interaction with a query like:

  SELECT * 
  FROM LogEntries
  WHERE TraceId = @TraceId

We also use a single connection and WAL, so we can write many thousands of entries per second if necessary.